Internal problem ID [8708]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 372.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-4 y^{3}+a y=-b} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 233
dsolve(diff(y(x),x)^2-4*y(x)^3+a*y(x)+b = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{6 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \frac {-i \sqrt {3}\, \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 i \sqrt {3}\, a -\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}-3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= -\frac {-i \sqrt {3}\, \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 i \sqrt {3}\, a +\left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {2}{3}}+3 a}{12 \left (27 b +3 \sqrt {-3 a^{3}+81 b^{2}}\right )^{\frac {1}{3}}} \\ y \left (x \right ) &= \operatorname {WeierstrassP}\left (x +c_{1} , a , b\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.421 (sec). Leaf size: 273
DSolve[b + a*y[x] - 4*y[x]^3 + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \wp (x-c_1;a,b) \\ y(x)\to \wp (x+c_1;a,b) \\ y(x)\to \frac {\left (\sqrt {81 b^2-3 a^3}+9 b\right )^{2/3}+\sqrt [3]{3} a}{2\ 3^{2/3} \sqrt [3]{\sqrt {81 b^2-3 a^3}+9 b}} \\ y(x)\to \frac {i \sqrt [3]{3} \left (\sqrt {3}+i\right ) \left (\sqrt {81 b^2-3 a^3}+9 b\right )^{2/3}-\sqrt [6]{3} \left (\sqrt {3}+3 i\right ) a}{12 \sqrt [3]{\sqrt {81 b^2-3 a^3}+9 b}} \\ y(x)\to \frac {\sqrt [3]{3} \left (-1-i \sqrt {3}\right ) \left (\sqrt {81 b^2-3 a^3}+9 b\right )^{2/3}-\sqrt [6]{3} \left (\sqrt {3}-3 i\right ) a}{12 \sqrt [3]{\sqrt {81 b^2-3 a^3}+9 b}} \\ \end{align*}